Multipeakons and a theorem of Stieltjes

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.Comment: 6 page

Fluid solid : can we converse with granite?

This investigation seeks to detect sources of the quantitative granite anomalies through various methods and use available resources to allow for an immersive, qualitative, and perhaps didactic experience, which will build a conceptual foundation for design of the in-between spaces made by the negative form of granite architectures. This thesis is about timescales and lenses by which to view them in partnership. With lenses are assumed perceptions, ones that define the understanding of the object in the viewfinder of the landscape, and in this case, the timescales which will be addressed in the following three phases: Phase 01 Background : Geological Time Phase 02 Registration : Atomic Time Phase 03 Where We Are : Human Tim

An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation

This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target keyword in an ordered list of the i-th block. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our argument shows that the multiple-block ordered search needs a large number of nonadaptive oracle queries on a black-box model of quantum computation that is also supplemented with advice. Our argument is also applied to the notions of computational complexity theory: quantum truth-table reducibility and quantum truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the 29th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27, 200

Of global reach yet of situated contexts: an examination of the implicit and explicit selection criteria that shape digital archives of historical newspapers

A large literature addresses the processes, circumstances and motivations that have given rise to archives. These questions are increasingly being asked of digital archives, too. Here, we examine the complex interplay of institutional, intellectual, economic, technical, practical and social factors that have shaped decisions about the inclusion and exclusion of digitised newspapers in and from online archives. We do so by undertaking and analysing a series of semi-structured interviews conducted with public and private providers of major newspaper digitisation programmes. Our findings contribute to emerging understandings of factors that are rarely foregrounded or highlighted, yet fundamentally shape the depth and scope of digital cultural heritage archives and thus the questions that can be asked of them, now and in the future. Moreover, we draw attention to providers’ emphasis on meeting the needs of their end-users and how this is shaping the form and function of digital archives. The end user is not often emphasised in the wider literature on archival studies and we thus draw attention to the potential merit of this vector in future studies of digital archives

Effects of Carbohydrates on Landing Mechanics and Postural Stability During Intermittent High-Intensity Exercise to Fatigue

Please refer to the pdf version of the abstract located adjacent to the title

Physical Performance Differences in Sea, Air and Land (SEAL) Operator Cohorts Separated by Demographics

Please refer to the pdf version of the abstract located adjacent to the title

Scalability of quantum computation with addressable optical lattices

We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size of quantum computations, arising in 3D optical lattices from current limitations on the ability to perform single qubit gates in parallel and in 2D lattices from constraints on laser power. Our results suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e., $\sim 10^6$ qubits) may be achievable, provided two-qubit gates can be performed with sufficiently high precision and degree of parallelizability. Parallelizability of long range interaction-based two-qubit gates is qualitatively compared to that of collisional gates. Different methods of performing single qubit gates are compared, and a lower bound of $1 \times 10^{-5}$ is determined on the error rate for the error mechanisms affecting $^{133}$Cs in a blue-detuned lattice with Raman transition-based single qubit gates, given reasonable limits on experimental parameters.Comment: 17 pages, 5 figures. Accepted for publication in Physical Review

Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.Comment: 20 page

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP